Refractive index and scattering effects on radiation in a semitransparent laminated layer

Heat transfer characteristics are analyzed for a laminated layer of two semitransparent scattering materials with refractive indices larger than one. Each side of the composite is heated by radiation and convection. Energy is transferred internally by conduction, emission, absorption, and isotropic scattering. The external surfaces of the composite and its internal interface are diffuse, which is intended to model composite ceramics in high-temperature applications. The two sublayers can have differing refractive indices greater than one. This causes internal reflection of some energy within the layers. Coupled with scattering, this has a substantial effect on the temperature distribution. Results are given for various optical thicknesses and refractive indices of the sublayers, and for scattering albedos up to one. Comparisons of numerical solutions are made with limiting cases based on the pure scattering, radiative diffusion, transparent, and opaque limits in the individual layers. The limiting solutions are very useful because they are convenient to evaluate and provide accurate results for many cases of interest.